#include <bits/stdc++.h>
#define maxn 1000007
#define int long long
#define dl long double
#define mod 1000000007
using namespace std;
int n, m;
inline int pls(int a, int b) {int m = a + b; return m < mod ? m : m - mod;}
inline int dec(int a, int b) {int m = a - b; return m < 0 ? m + mod : m;}
inline int mul(int a, int b) {return 1ll * a * b % mod;}
inline int fpow(int a, int b) {
  int ans = 1;
  for(; b; b >>= 1,a = mul(a, a)) if(b & 1) ans = mul(ans, a);
  return ans;
}
inline int inv(int a) {return fpow(a, mod - 2);}
inline int dvi(int a, int b) {return mul(a, inv(b));};
inline int qread() {
  char c = getchar(); int num = 0, f = 1;
  for(; !isdigit(c); c=getchar()) if(c == '-') f = -1;
  for(; isdigit(c); c=getchar()) num = num * 10 + c - '0';
  return num * f;
}
struct Node{
  int to, nxt;
}e[maxn * 2];
int h[maxn], cnt;
void add(int a, int b) {
  e[++cnt] = {b, h[a]};
  h[a] = cnt;
}
inline bool cmp(int a, int b) {
  return a > b;
}
int height[maxn], top[maxn], son[maxn];
void geth(int u) {
  int to;
  son[u] = height[u] = 0;
  for(int i = h[u]; i; i = e[i].nxt) {
    to = e[i].to;
    geth(to);
    if(height[to] > height[u]) {
      son[u] = to;
      height[u] = height[to];
    }
  }
  height[u]++;
}
void dfs(int u, int t) {
  top[u] = t;
  if(!son[u]) return;
  dfs(son[u], t);
  for(int i = h[u]; i; i = e[i].nxt) {
    int to = e[i].to;
    if(to == son[u]) continue;
    dfs(to, to);
  }
}
int d[maxn], tot;
void solve() {
  cnt = 0;
  n = qread();
  tot = 0;
  for(int i = 1; i <= n; i++) {
    height[i] = h[i] = 0;
  }
  for(int i = 2; i <= n; i++) {
    add(qread(), i);
  }
  geth(1);
  dfs(1, 1);
  for(int i = 1; i <= n; ++i) {
    if(top[i] == i) d[++tot] = height[i];
  }
  sort(d + 1, d + 1 + tot, cmp);
  int res = 0x6f6f6f6f6f6f6f6f;
  d[tot + 1] = 0;
  for(int i = 0; i <= tot; ++i) {
    res = min(res, i + d[i + 1]);
//    cout << i << " :"<< i + d[i + 1] << '\n';
  }
  cout << res << '\n';
}
signed main() {
  int q = qread();
  while(q--) {
    solve();
  }
  return 0;
}